In this paper we study the Gross-Pitaevskii equation of the theory of superfluidity, i.e., the nonlinear Schrödinger equation of the Ginzburg-Landau type. We investigate the dynamics of the breakup of the double vortex. More specifically, we prove instability of the double vortex, compute the complex eigenvalue responsible for this instability, and derive the dynamical equation of motion of (centers of) single vortices resulting from splitting of the double vortex. We expect that our analysis can be extended to vortices of higher degree and to magnetic and Chern-Simmons vortices. Copyright © 2011 American Institute of Physics.